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Piecewise monotone functions
Wellbehaved piecewise monotone functions
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88 Lemma Banach Spaces behaviour component contains a dense continuous functions countable dense in 0,1 dense open subset disjoint Edited end-point exists f is central f is increasing f satisfies fk(x fm(J fm(x fm(z fn is monotone fn(J fn(x follows functions f g has property gives hence holds Homt(f homterval implies infinite register shift int(D)uint(E int(J iterates of functions largest interval containing Lebesgue measure Let f e linear fractional transformations mean value theorem monotone functions Note one-sided stable Per(n.f periodic orbit periodic with period point of f points in a,b Proceedings Proof Let proof of Proposition proof of Theorem property Q Proposition 4.6 Ps(f reduction of 0,1],f regular resp Schwarzian derivative Section simple reduction sink of f subset of 0,1 Theorem 5.2 topologically conjugate Trap(f)uHomt(f turning point unstable periodic point